Question

Three solid spheres of radii 6 cm, 8 cm and 10 cm are melted to form a sphere. The radius of the sphere so formed is

(a) 24 cm
(b) 16 cm
(c) 14 cm
(d) 12 cm

Answer 1

(d) 12 cm

Radius (r₁) of 1^st sphere = 6 cm
Radius (r₂) of 2^nd sphere = 8 cm
Radius (r₃) of 3^rd sphere = 10 cm
Let the radius of the resulting sphere be r.
We know that the object formed by recasting these spheres will be same in volume as the sum of the volumes of these spheres. Volume of 3 spheres = Volume of resulting sphere
$\frac{4}{3}\mathrm{\pi }\left[{r_1}^3+{r_2}^3+{r_3}^3\right]=\frac{4}{3}{\mathrm{\pi r}}^3$
$\Rightarrow \frac{4}{3}\mathrm{\pi }\left[6^3+8^3+{10}^3\right]=\frac{4}{3}{\mathrm{\pi r}}^3$
⇒ r³ = (216 + 512 + 1000) = 1728
⇒ r = 12 cm
Hence, the radius of the sphere so formed is 12 cm.